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Acta Physica Sinica

The evolution property of three-body entanglement measure in Tavis-Cummings mode l

Zuo Zhan-Chun, Yun‐Jie Xia, 曲阜师范大学物理系,曲阜 273165

Published Jan 1, 2003• 13 citations
Publisher

Abstract

This paper studies the quantum entanglement of the Tavis-Cummings model for two steady identical two-level atoms interac-ting with a single-mode field. Whe n the field is vacuum and the two atoms stay in Einstein-Podolsky-Rosem entangle d state or disentangled state initially, we obtain that the system will evol ve to a three-body approximate W entangled state. The entanglement measure will change with the variation of system initial state, coupling coefficients, detuni ng degree and atomic population inversion. It should be noted that the atomic co upling coefficient exhibits the nonlinear effect and the entanglement measure os cillates periodically in accordance with atomic population inversion.

DOI
10.7498/aps.52.2687

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This paper studies the quantum entanglement of the Tavis-Cummings model for two steady identical two-level atoms interac-ting with a single-mode field. Whe n the field is vacuum and the two atoms stay in Einstein-Podolsky-Rosem entangle d state or disentangled state initially, we obtain that the system will evol ve to a three-body approximate W entangled state. The entanglement measure will change with the variation of system initial state, coupling coefficients, detuni ng degree and atomic population inversion. It should be noted that the atomic co upling coefficient exhibits the nonlinear effect and the entanglement measure os cillates periodically in accordance with atomic population inversion.
The quantum entanglement of the Tavis-Cummings model for two identical two-level atoms interacting with a single-mode field is considered.When the field is one photon and the two atoms stay in ground states initially,it is abtained that the system will evolve to a three-body approximate state.The result shows that every entanglement measure of the system will be reduced when atomic coupling coefficient is larger than coupling coefficient between field and atom,and the entanglement measure of atoms and the entanglement measure between two atoms with field will be reduced more quickly.Meanwhile,every entanglement measure periodic will be also shortened relevantly.
In light of quantum theory,we investigate the entanglement properties of two entangled two-level atoms that interact resonantly with a single-mode vacuum field with atomic motion.The results show that if the two atoms are prepared in maximun entangled(EPR)state initially,the maximum of three-body entanglement measure is equated with the perfect three-body W entangled state.The parameter of field-mode structure p influences the time evolution osciuation property of three-body entlinglement measure,with the gradually increasing of p,the average of three-body entanglement measure will gradually decrease,three-body entangled state will tend to disentangled state inch by inch.
The case that one of the two entangled identical two-level atoms interacts with a single-mode field among three-body entanglement was mainly considered. The results show that in initial the more the degree of entanglement of the two entangled atoms have, the more oscillation of the entanglement measure will have,and the more times of the maximally entanglement measure will obtain. Meanwhile, it was found that entanglement measure will be reduced when atomic coupling coefficient is larger than coupling coefficient between field and atom.
We investigate the entanglement time evolution of two entangled two-level atoms that interact resonantly with a single-mode field in the Fock state. The results show that the two-atom entanglement state appears with periodicity. The influence of the two-atom initial state, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the entanglement degree of two atoms are revealed. Meanwhile the two-atom quantum state will forever stay in the maximum entangled state when the initial state is proper.
The three-qubit entangled state in Tavis-Cummings model for two identically steady two-level atoms interacting with single mode field can be generated when the atom-field interaction is far from atom-atom interaction.By analyzing three-qubit entanglement of the system,we obtain that the entanglement of the system will change with the variation of system initial state,coupling coefficients between atom and field or atoms.Especially,when the initial state is special,the system will stay in W-entangled state.The necessary condition for generating W-state is that the coupling constant between two atoms is more less than that of between an atom and field.
Atomic evolution properties of entanglement are represented by concurrence,and the effects of atoms-coupling on the properties are considered within the context of the Tavis-Cummings model.Two coupling two-level atoms interact with a quantized cavity field,and the explicit forms of the evolution operator are given.It is found that atomic entanglement can always be kept though atoms are initially unentangled.The results also show that the amplitude of the entanglement evolution oscillation increases,and the periods of the oscillation become longer with increasing atomic coupling effect.When atomic coupling is strong enough,atomic entanglement evolution behavior is similar to that of the Heisenberg model.Atomic entanglement evolution properties have relations with atomic population.